Hi Shelby !
For stage one...it is not required at all to visit an ATC unit, and I'm not sure it's possible. I'm almost 100% positive you wouldn't be allowed to visit a centre unless your about to sit the 3rd stage. To find out about it, it's searching online and reading books I'm afraid.
My maths skills were next to nothing....but I really found the speed distance time questions on the RAF website to be the most helpful.
I have not completed uni positions or fancy qualifications or anything like that..I work in a bar and I'm going on to stage 2 on the 3rd of May. Don't let it put you off !!
NATS will not take in to consideration spending that amount of money getting there, unfortunately. For stage 1...if you meet the required pass marks, you'll get invited to stage 2. Just study study study and that will be impressive enough.
The centre is walking distance from the airport....but that's a lonnnng 20-30 minute walk. Get a taxi, shouldn't cost you too much, and they should know where it is (it's surprisingly difficult to find!).
Hope this helps....go for it and good luck !!